Previous benchmarks of orbital-optimized density functional calculations of transition intensities in molecules have primarily been restricted to the lowest electronic excitation. Here, the performance of this variational approach is assessed across several valence and Rydberg excited states of small molecules, calculating the absorption spectra up to 10 eV. A plane-wave basis set is employed to accurately describe diffuse Rydberg excitations, while the transition dipole moment is evaluated from nonorthogonal Kohn–Sham determinants within the projector augmented wave formalism. Comparison with higher-level coupled-cluster results shows that orbital-optimized calculations provide a good description of oscillator strengths for states with predominantly single-configurational character, even with the generalized gradient approximation functional PBE. The inclusion of exact exchange and self-interaction correction further improves the results, with the latter yielding the smallest errors (mean absolute relative error of ∼25%). In contrast, large errors for all functionals are found for multi-configurational states, due to an inability of the approach to describe the multi-configurational character. Nonorthogonality between independently optimized states has previously been raised as a possible source of error in transition properties. In the present benchmark, no correlation of the nonorthogonality between the ground and excited states with the error on the transition intensity is found. These results establish the performance of orbital-optimized density functional calculations for absorption spectra of small molecules and highlight the need for extensions that combine state-specific orbital relaxation with a multi-configurational treatment.